Finite Group Databasebeta

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C₂×#4658 #73345

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

604 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 25 points:

(1,2)(3,4,5)(7,8)(10,12,13,16)(11,15,14,17)(18,20)(19,22)(21,24)(23,25);(6,8,9,7)(10,11)(12,15)(13,14)(16,17)(18,19,21,23)(20,22,24,25);(4,5)(6,7,9,8)(11,14)(12,16)(20,24)(22,25);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5921);